I neglected to mention that, once you get either I_theta or some empirical
estimate
of it, you then invert it to get an estimate of the asymptotic covariance
matrix of the
MLE.
On Tue, Jan 22, 2013 at 3:48 PM, Mark Leeds <marklee...@gmail.com> wrote:
> Hi Doug: I was just looking at this coincidentally. When X is a vector,
> the Fisher Information I_{theta} = the negative expectation of the second
> derivatives of the log likelihood. So it's a matrix. In other words,
> I_theta = E(partial^2 /partial theta^2(log(X,theta).) where X is a vector.
>
> But, even though the the Fisher Information has a seemingly nice formula,
> ( and this is where my confusion arose when I was dealing with this and why
> I'm looking at it right
> now. I have short document that I wrote to myself explaining it so if
> anyone wants it, email me individually. It's nothing earth shattering !!!!!
> ) in many cases taking the that expectation is not easy so the Fischer
> Information is approximated by its empirical counterpart which is obtained
> by summing each of the elements in the matrix given the n observations and
> then dividing each of the elements in the matrix by n.
>
>
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> On Tue, Jan 22, 2013 at 3:27 PM, Douglas Bates <ba...@stat.wisc.edu>wrote:
>
>> Your question is better addressed to the R-help@R-project.org mailing
>> list,
>> which I am copying on this reply.
>>
>> You are confusing a statistical concept, the Fisher Information matrix,
>> with a numerical concept, the Hessian matrix of a scalar function of a
>> vector argument.
>>
>> The Fisher information matrix is the Hessian matrix of a particular
>> function at its optimum and I have forgotten whether that function is the
>> log-likelihood or negative twice the log-likelihood or ... Rather than
>> get
>> it wrong I am sending a copy of this reply to the list where many of the
>> readers will be able to answer you more reliably than I can.
>>
>>
>> On Tue, Jan 22, 2013 at 1:22 PM, Marcos Coque Jr <mcoqu...@yahoo.com.br
>> >wrote:
>>
>> > Dear Bates,
>> >
>> > I am using the fdHess function for R language.
>> > And I have a question.
>> >
>> > What is the relationship with the Hessian and Fisher Information in your
>> > function?
>> > Because I think that Fisher Information=-Hessian, but I found the
>> oposite
>> > in your function.
>> > Maybe I be something wrong...
>> >
>> > Thanks,
>> >
>> > Marcos
>> >
>>
>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
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>> PLEASE do read the posting guide
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>>
>
>
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